They have been told by a QC representing the celebrity that discharging the injunction would have "devastating consequences".

Thursday's proceedings before the panel of judges, headed by the court's president Lord Neuberger, follow a decision by Court of Appeal judges on Monday in favour of the tabloid's publishers, News Group Newspapers.

Earlier this year The Sun on Sunday wanted to publish an account of the man's alleged extra-marital activities, but he argued that he had a right to privacy and took legal action.

The newspaper won the first round in January when a High Court judge refused to impose an injunction barring publication.

But the man challenged that decision and two appeal court judges ruled in his favour. Lord Justice Jackson and Lady Justice King imposed an injunction preventing the newspaper from identifying the man in an article.

Lawyers for the publishers asked the same two judges, sitting with Lord Justice Simon, to lift the ban after the man's identity emerged online.

They told the three judges that the ban should end because he had been named in articles abroad – outside the legal jurisdiction of England and Wales – and his name could be found on the internet. The man opposed the application and said the ban should stay.

On Monday the three judges ruled the injunction should be lifted, but they said it should stay in place pending an application by the man to the Supreme Court.

A Supreme Court spokeswoman said the injunction will remain in place at least until the conclusion of the hearing before the justices.

Judges have said that the man, referred to as PJS, is in the entertainment business and that his spouse – referred to as YMA – is also well-known in the industry and that the couple had ''young'' children.

Desmond Browne QC, for the celebrity, told Lord Neuberger, deputy president Lady Hale, Lord Mance, Lord Reed and Lord Toulson that the discharge of the injunction would have just as "devastating consequences" for PJS and his children now as in January.

He said the need for the protection of information and identity of PJS may have been diminished but it had not been extinguished, and the need for protection from intrusion remained as great, if not greater, in the light of the events of the past fortnight.

He added there was a need to protect the children from harassment and increased press attention.

"That is an issue not just now but for the future when they grow up."

There would be a "storm of harassment" if the injunction was lifted, he added.

He said it was hard to see that the Court of Appeal had afforded the children "the primacy of importance" to which they were entitled.